Question

The amount of an ordinary $7,500.00 annuity for 3 years at 12 percent compounded quarterly is

Answer 1

`\bf \qquad \qquad \textit{Future Value of an ordinary annuity}\\ \left. \qquad \qquad \right.(\textit{payments at the end of the period}) \\\\ A=pymnt\left[ \cfrac{\left( 1+(r)/(n) \right)^(nt)-1}{(r)/(n)} \right]`


`\bf \qquad \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array} & \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to &7500\\ r=rate\to 12\%\to (12)/(100)\to &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four times} \end{array}\to &4\\ t=years\to &3 \end{cases} \\\\\\ A=7500\left[ \cfrac{\left( 1+(0.12)/(4) \right)^(4\cdot 3)-1}{(0.12)/(4)} \right]`

Answer 2

$180,997.50.

Explanation:

1. On TABLE 14-1 Future Value of $1.00 Ordinary Annuity, select the periods row corresponding to the number of interest periods.

2. Select the rate-per-period column corresponding to the period interest rate.

3. Locate the value in the cell where the periods row intersects the rate-per-period column.

4. Multiply the annuity payment by the table value from step 3.

Future value = annuity payment × table value

FV = $7500.00 * 24.133 = $180,997.50